PROBLEM 6. 10 A histogram has mean 70 and standard deviation 5 If the histogram is not bell shaped but it is symmetric. Find the least proportion of data falls between 70 and 80 If the histogram is bell shaped. Find the proportion of data between 65 and 77
Answers
Answer:
a. 0.4772 = 47.72 %
b. 0.7605 = 76.05 %
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
a. ind the least proportion of data falls between 70 and 80 If the histogram is bell shaped:
So for 70 copies we have:
z = (70 - 70) / (5)
z = 0
and this value represents 0.5
So for 80 copies we have:
z = (80 - 70) / (5)
z = 2
and this value represents 0.9772
p (70 > x > 80) = 0.9772 - 0.5
p (70 > x > 80) = 0.4772 = 47.72 %
b. Find the proportion of data between 65 and 77
So for 65 copies we have:
z = (65 - 70) / (5)
z = -1
and this value represents 0.1587
So for 77 copies we have:
z = (77 - 70) / (5)
z = 1.4
and this value represents 0.9192
p (65 > x > 77) = 0.9192 - 0.1587
p (65 > x > 77) = 0.7605 = 76.05 %
Related Questions
A laptop computer is purchased for $2300. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Answers
Answer:
after the 1st year
Step-by-step explanation:
$2300 × 75% = $1725.00
$2300-$1725= $575
which of the following is equivalent to this?
a: b over a divided by d over c
b: a over b divided by d over c
c: b over a divided by d over c
d: b over a divided by c over d
please help me!
Answers
Answer:
b: a over b divided by do over c
Step-by-step explanation:
You can solve this by plugging in numbers for each variable.
For example: a=1, b=4, c=1, d=2
1/4 ÷ 1/2 = 0.125
If you plug in the numbers for all the equations listed, only 1/4 ÷ 2/1 = 0.125.
Plz help for 80 points question is attached
Answers
Answer:
2 and 256
Step-by-step explanation:
Check the attachment
Answer:
2 and255
Step-by-step explanation:
look atyourquestion
I need help for the solution
Answers
Answer:
[tex]\boxed{ \ dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t\ }[/tex]
Step-by-step explanation:
it is a long time I have not applied Ito's lemma
I would say the following
for [tex]f(x)=x^2[/tex]
f'(x)=2x
f''(x)=2
so using Ito's lemma we can write that
[tex]dY_t=2V_tdV_t+\phi^2dt[/tex]
[tex]dY_t=2(\theta+\psi V_t^2)dt+2\phi V_tdW_t+\phi^2dt[/tex]
[tex]dY_t=(2\theta+2\psi V_t^2+\phi^2)dt+2\phi V_tdW_t[/tex]
so it comes
[tex]dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t[/tex]
Find the area of a triangle that has the base of 5 inches and a height of 3 3/4 inches
Answers
Answer:
9.375 in^2
Step-by-step explanation:
Need help with this . The picture is enclosed
Answers
Answer: (fоg)(24)=5
Step-by-step explanation:
(fоg)(24) is f of g of 24. This means you plug in g(24) into f(x).
[tex]g(24)=\sqrt{24-8}[/tex]
[tex]g(24)=\sqrt{16}[/tex]
[tex]g(24)=4[/tex]
Now that we know g(24), we can plug it into f(x).
f(4)=2(4)-3
f(4)=8-3
f(4)=5
Two thousand dollars is deposited into a savings account at 8.5% interest compounded continuously. (a) What is the formula for A(t), the balance after t years? (b) What differential equation is satisfied by A(t), the balance after t years? (c) How much money will be in the account after 5 years? (d) When will the balance reach $3000? (e) How fast is the balance growing when it reaches $3000?
Answers
Answer:
a)[tex]A(t)=2000e^{0.085t}[/tex]
b)[tex]A'(t)=170e^{0.085t}[/tex]
c)$3059.1808
d)t=4.77 years
e) The balance growing is $254.99/year
Step-by-step explanation:
We are given that Two thousand dollars is deposited into a savings account at 8.5% interest compounded continuously.
Principal = $2000
Rate of interest = 8.5%
a) What is the formula for A(t), the balance after t years?
Formula [tex]A(t)=Pe^{rt}[/tex]
So,[tex]A(t)=2000e^{0.085t}[/tex]
B)What differential equation is satisfied by A(t), the balance after t years?
So, [tex]A'(t)=2000 \times 0.085 e^{0.085t}[/tex]
[tex]A'(t)=170e^{0.085t}[/tex]
c)How much money will be in the account after 5 years?
Substitute t = 5 in the formula "
[tex]A(t)=2000e^{0.085t}\\A(5)=2000e^{0.085(5)}\\A(5)=3059.1808[/tex]
d)When will the balance reach $3000?
Substitute A(t)=3000
So, [tex]3000=2000e^{0.085t}[/tex]
t=4.77
The balance reach $3000 in 4.77 years
e)How fast is the balance growing when it reaches $3000?
Substitute the value of t = 4.77 in derivative formula :
[tex]A'(t)=170e^{0.085t}\\A'(t)=170e^{0.085 \times 4.77}\\A'(t)=254.99[/tex]
Hence the balance growing is $254.99/year
A 12 ft ladder leans against the side of a house. The top of the ladder is 10ft off the ground. Find x, the angle of elevation of the ladder.
1. Remember to address each of the critical elements of the prompt:
Articulate your overall approach to solving this problem before tackling the details. In other words, think about what the question is actually asking, which pieces of information are relevant, and how you can use what you have learned to fill in the missing pieces.
2. Apply the mathematical process to solve the problem:
Interpret the word problem to identify any missing information.
Translate the word problem into an equation.
Appropriately use the order of operations and law of sines and cosines to determine the solution.
Check your work by ensuring that the known properties of triangles are met.
Answers
The image is missing, so i have attached it.
Answer:
x = 56.44°
Step-by-step explanation:
From the attached image, we can see that this is a right angle triangle which has opposite, adjacent and hypotenuse as sides. Since we want to find the angle x, thus, we can make use of trigonometric ratios.
From the attached image, the side opposite to angle x is 10ft and the hypotenuse is 12 ft.
From trigonometric ratios, we know that, sin x = opposite/hypotenuse
So, sin x = 10/12
x = sin^(-1) (10/12)
x = sin^(-1) 0.8333
x = 56.44°
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged.
Number of Hours Frequency Amount Charged
1 21 $4
2 36 6
3 53 9
4 40 13
5 22 14
6 11 16
7 9 18
8 36 22
228
A. Convert the information on the number of hours parked to a probability distribution. Is this a discrete or a continuous probability distribution?
B. Find the mean and the standard deviation of the number of hours parked. How would you answer the question: How long is a typical customer parked?
C. Find the mean and the standard deviation of the amount charged.
Answers
Answer: A. This is a discrete probability distribution.
hours probability
1 0.09
2 0.16
3 0.23
4 0.17
5 0.09
6 0.05
7 0.04
8 0.16
B. E(X) = 4.12; σ = 2.21
C. μ = 12.75; s = 6.11
Step-by-step explanation: Probability Distribution is an equation or table linking each outcome of an experiment with its probability of ocurrence. For this case, since the experiment is performed a high number of times and in a long run, the relative frequency of the event is its probability. Therefore:
A. To convert to a probability distribution, find the probability through the frequency by doing:
Hour 1
P(X) = [tex]\frac{21}{228}[/tex] = 0.09
Hour 2
P(X) = [tex]\frac{36}{228}[/tex] = 0.16
Hour 3
P(X) = [tex]\frac{53}{228}[/tex] = 0.23
Hour 4
P(X) = [tex]\frac{40}{228}[/tex] = 0.17
Hour 5
P(X) = [tex]\frac{22}{228}[/tex] = 0.09
Hour 6
P(X) = [tex]\frac{11}{228}[/tex] = 0.05
Hour 7
P(X) = [tex]\frac{9}{228}[/tex] = 0.04
Hour 8
P(X) = [tex]\frac{36}{228}[/tex] = 0.16
The table will be:
hours probability
1 0.09
2 0.16
3 0.23
4 0.17
5 0.09
6 0.05
7 0.04
8 0.16
This is a discrete distribution because it lists all the possible values that the discrete variable can be and its associated probabilities.
B. Mean for a probability distribution is calculated as:
E(X) = ∑[[tex]x_{i}[/tex].P([tex]x_{i}[/tex])]
E(X) = 1*0.09 + 2*0.16+3*0.23+4*0.17+5*0.09+6*0.05+7*0.04+8*0.16
E(X) = 4.12
Standard Deviation is:
σ = √∑{[x - E(x)]² . P(x)}
σ = [tex]\sqrt{(1-4.12)^{2}*0.09 + (2-4.12)^{2}*0.16 + ... + (7-4.12)^{2}*0.04 + (8-4.12)^{2}*0.16}[/tex]
σ = [tex]\sqrt{4.87}[/tex]
σ = 2.21
The average number of hours parked is approximately 4h with a standard deviation of approximately 2 hours, which means that a typical costumer parks between 2 to 6 hours.
C. Mean for a sample is given by: μ = ∑[tex]\frac{x_{i}}{n}[/tex] , which is this case is:
μ = [tex]\frac{4+6+9+13+14+16+18+22}{8}[/tex]
μ = 12.75
Standard Deviation of a sample: s = √[tex]\frac{1}{n-1}[/tex]∑([tex]x_{i}[/tex] - μ)²
s = [tex]\sqrt{ \frac{(4-12.75)^{2} + (6-12.74)^{2} + ... + (18-12.75)^{2} + (22-12.75)^{2} }{8-1}}[/tex]
s = 6.11
The average amount charged is 12.75±6.11.
The manager of a coffee shop wants to know if his customers’ drink preferences have changed in the past year. He knows that last year the preferences followed the following proportions – 34% Americano, 21% Cappuccino, 14% Espresso, 11% Latte, 10% Macchiato, 10% Other. In a random sample of 450 customers, he finds that 115 ordered Americanos, 88 ordered Cappuccinos, 69 ordered Espressos, 59 ordered Lattes, 44 ordered Macchiatos, and the rest ordered something in the Other category. Run a Goodness of Fit test to determine whether or not drink preferences have changed at his coffee shop. Use a 0.05 level of significance. Americanos Capp. Espresso Lattes Macchiatos Other Observed Counts 115 88 69 59 44 75 Expected Counts 153 94.5 63 49.5 45 45 Enter the p-value - round to 5 decimal places. Make sure you put a 0 in front of the decimal. P-value =
Answers
Answer:
Step-by-step explanation:
[tex]H_0 : \texttt {null hypothesis}\\\\H_1 : \texttt {alternative hypothesis}[/tex]
The null hypothesis is the drink preferences are not changed at coffee shop.
The alternative hypothesis is the drink preferences are changed at coffee shop.
the level of significance = α = 0.05
We get the Test statistic
[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex]
Where, [tex]F_o[/tex] is observed frequencies and
[tex]F_e[/tex] is expected frequencies.
N = 6
Degrees of freedom = df = (N – 1)
= 6 – 1
= 5
the level of significance α = 0.05
Critical value = 11.07049775
( using Chi square table or excel)
Tables for test statistic are given below
F_o F_e Chi square
Americanos 115 153 9.4379
Capp. 88 94.5 0.447
Espresso 69 63 0.5714
Lattes 59 49.5 1.823
Macchiatos 44 45 0.022
Other 75 45 20
Total 450 450 32.30
[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex] = 32.30
P-value = 0.00000517
( using Chi square table or excel)
P-value < α = 0.05
So, we reject the null hypothesis
This is because their sufficient evidence to conclude that Drink preferences are changed at coffee shop.
Someone flips five coins, but you don’t see the outcome. The person reports that no tails are showing. What is the probability that the person flipped 5 heads?
Answers
Answer:
0.03125 = 3.125% probability that the person flipped 5 heads
Step-by-step explanation:
For each coin, there are only two possible outcomes. Either it was heads, or it was tails. The result of a coin toss is independent of other coin tosses. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Five coins:
This means that n = 5.
Fair coin:
Equally as likely to be heads or tails, so p = 0.5.
What is the probability that the person flipped 5 heads?
This is P(X = 5).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
0.03125 = 3.125% probability that the person flipped 5 heads
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answers
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?
Answers
Answer:
5/33649= approx 0.00015
Step-by-step explanation:
Total number of outcomes are C24 6= 24!/(24-6)!/6!=19*20*21*22*23*24/(2*3*4*5*6)= 19*14*22*23
Half of the Committee =3 persons. That mens that number of the women in Commettee=3. 3 women from 6 can be elected C6 3 ways ( outputs)=
6!/3!/3!=4*5*6*/2/3=20
So the probability that 3 members of the commettee are women is
P(women=3)= 20/(19*14*22*23)=5/(77*19*23)=5/33649=approx 0.00015
The probability that precisely half of the members will be women is;
P(3 women) = 0.1213
This question will be solved by hypergeometric distribution which has the formula;
P(x) = [S_C_s × (N - S)_C_(n - s)]/(NC_n)
where;
S is success from population
s is success from sample
N is population size
n is sample size
We are give;
s = 3 women (which is precisely half of the members selected)
S = 6 women
N = 24 men and women
n = 6 people selected
Thus;
P(3 women) = (⁶C₃ * ⁽¹⁸⁾C₍₃₎)/(²⁴C₆)
P(3 women) = (20 * 816)/134596
P(3 women) = 0.1213
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A car can travel 45 miles on 2 gallons of gasoline. How far can it travel on 5.6
gallons?
Answers
Answer:
It can travel 45 / 2 = 22.5 miles per gallon so the answer is 22.5 * 5.6 = 126 miles.
Please answer this correctly
Answers
Answer:
1/2 (simplified)
Step-by-step explanation:
6 numbers (that's the total probability) --> 6 denominator
3 are odd (odd numbers in the probability) --> 3 numerator
so => 3/6
--> simplify
1/2
Hope this helps!
Answer: 1/2
Please answer this correctly
Answers
Answer:
yes
Step-by-step explanation:
not every person is going to have the same opinion, so it is yes.
// have a great day //
Answer:
Yes, because if Pedro asked them the question "what do you think of public transportation?" the majority would probably say that they like it or something along those lines. This is biased because there may be other city inhabitants who don't think very highly of public transportation. Basically, what I'm trying to say is that not everyone will have the same opinion.
When $\frac{1}{1111}$ is expressed as a decimal, what is the sum of the first 40 digits after the decimal point?
Answers
Answer:
90
Step-by-step explanation:
1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)
Number of digits 9:
40/4= 1010*9= 90Answer:
90
Step-by-step explanation:
two sides of a parallelogram meet at an angle of 50 degrees. If the length of one side is 3 meters and the length of the other side is 5 meters, find the length of the longest diagonal and the angles that it forms with each of the given sides.
Answers
Answer:
The longer diagonal has a length of 7.3 meters.
The angles are 31.65° and 18.35°
Step-by-step explanation:
If one angle of the parallelogram is 50°, another angle is also 50° and the other two angles are the supplement of this angle. so the other three angles are:
50°, 130° and 130°.
The longer diagonal will be the one opposite to the bigger angle (130°), and this diagonal divides the parallelogram in two triangles.
Using the law of cosines in one of these two triangles, we have:
[tex]diagonal^2 = a^2 + b^2 - 2ab*cos(130\°)[/tex]
[tex]diagonal^2 = 3^2 + 5^2 - 2*3*5*(-0.6428)[/tex]
[tex]diagonal^2 = 53.284[/tex]
[tex]diagonal = 7.3\ meters[/tex]
So the longer diagonal has a length of 7.3 meters.
To find the angles that this diagonal forms with the sides, we can use the law of sines:
[tex]a / sin(A) = b/sin(B)[/tex]
[tex]5 / sin(A) = diagonal / sin(130)[/tex]
[tex]sin(A) = 5 * sin(130) / 7.3[/tex]
[tex]sin(A) = 0.5247[/tex]
[tex]A = 31.65\°[/tex]
The other angle is B = 50 - 31.65 = 18.35°
Please check the image attached for better comprehension.
Black walnut trees contain chemicals that inhibit the growth of other plants. In a simple experiment to test whether this is true, you grow several tomato plants in soil with and without decomposing leaves from a black walnut tree. You collect data on plant height as a measure of growth. In this experiment, __________ is the independent variable, __________ is the dependent variable, and __________ is the control.
Answers
Answer:
Height of tomato plant is the dependent variable
Presence of walnut leaves in the soil is the independent variable
Tomato plants grown without walnut leaves is the control
Step-by-step explanation:
An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment. In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.
A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment. In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.
A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time. Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.
Consider random samples of size 900 from a population with proportion 0.75 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places. standard error
Answers
Answer:
[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]
And replacing we got:
[tex] SE=\sqrt{\frac{0.75*(1-0.75)}{900}}= 0.014[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n=900[/tex] represent the sample size selected
[tex]p = 0.75[/tex] represent the population proportion
We want to find the standard error and we can use the distribution for the sample proportion and for this case since the sample size is large enough and we satisfy np>10 and n(1-p) >10 we have:
[tex] \hat p \sim N (p,\sqrt{\frac{p(1-p)}{n}})[/tex]
And the standard error is given;
[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]
And replacing we got:
[tex] SE= \sqrt{\frac{0.75* (1-0.75)}{900}}= 0.014[/tex]
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim. (a) Which form of the hypotheses should be used to test the manager's claim? H0: - Select your answer - Ha: - Select your answer - The member of the hotel's accounting staff suspects that the total charges for guest bills have Select in recent months. To test the manager’s claim, the staff member will conduct Select test of the population Select . (b) What conclusion is appropriate when H0 cannot be rejected? When H0 cannot be rejected, there Select enough evidence to conclude that the total charges for guest bills have Select in recent months. (c) What conclusion is appropriate when H0 can be rejected? When H0 can be rejected, there Select enough evidence to conclude that the total charges for guest bills have Select in recent m
Answers
Answer:
a) Null hypothesis (H0): the mean guest bill for a weekend is $600.
Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.
b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600.
c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.
Step-by-step explanation:
a) The accountant, as he wants to see if there is evidence to support the claim that the mean guest bill has increased significanty, should write the hypothesis like that:
Null hypothesis (H0): the mean guest bill for a weekend is $600.
Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.
A sample of bills of the period in study needs to be taken in order to have a representation of the actual population of bills and then perform a t-test, as the sample mean and standard deviation will be used to perform the test.
b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600. If the P-value was low but not enough, they may take another sample to perform the test again or leave it like that.
c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.
george cut a cake into 8 equal pieces. what is the unit fraction for the cake
Answers
Answer: 1/8
Step-by-step explanation:
Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.
Hope this helps! Please mark as brainliest!
The unit fraction of the cake is 1/8
What is a unit fraction?A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.
Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake
Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.
Hence, the unit fraction of the cake is 1/8
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Find the area of the smaller sector.
A
6 in
030°
Area = [? ]in?
B
Round your answer to the nearest hundredth.
Answers
Answer:
9.42 in²
Step-by-step explanation:
The area of whole circle S=pi*R² , where pi is appr. 3.14, R= 6 in
S= 3.14*6² =113.04 in²
The area of smaller sector is Ssec=S/360*30=113,04/12=9.42 in²
The area of the smaller sector with a central angle of 30 degrees and a radius of 6 inches is 9.42478 square inches.
To find the area of a sector, you can use the formula:
Area of sector = (θ/360) × π × r²
where θ is the central angle in degrees, r is the radius of the sector.
The central angle is 30 degrees and the radius is 6 inches.
Plugging these values into the formula:
Area of sector = (30/360) × π × 6²
= (1/12) × π × 36
= (1/12) × 3.14159 × 36
= 9.42478 square inches
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Number of multiples of 7 between 200 and 1000
Answers
Answer:
114
Step-by-step explanation:
Answer:
144Step-by-step explanation:
Teaching descriptive statistics. A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.
a. What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?
b. What are the degrees of freedom associated with the F-test for evaluating these hypotheses?
c. Suppose the p-value for this test is 0.0168. What is the conclusion?
Answers
Answer:
Step-by-step explanation:
a. The hypotheses are:
Null hypothesis: the average test scores are the same for the different teaching methods.
Alternative hypothesis: the average test scores are different for the different teaching methods.
b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample
c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.
Can someone answer this question for me pleas?
Answers
Answer:
Step-by-step explanation:
The justification of each given statements in the question are:
11) F. Definition of right angle.
12) D. Definition of supplementary <'s.
13) A. Definition of congruence.
14) C. Definition of complementary <'s.
15) L. Congruent supplementary theorem
16) H. Vertical angle theorem.
17) G. Angle addition postulate.
18) J. Supplementary theorem.
The mean number of hours of part-time work per week for a sample of 317 teenagers is 29. If the margin of error for the population mean with a 95% confidence interval is 2.1, construct a 95% confidence interval for the mean number of hours of part-time work per week for all teenagers.
Answers
Answer:
The degrees of freedom are given by:
[tex]df=n-1=317-1=316[/tex]
And replaicing we got:
[tex]29-2.1=26.9[/tex]
[tex]29+2.1=31.1[/tex]
The 95% confidence interval would be between 26.9 and 31.1
Step-by-step explanation:
Information given
[tex]\bar X= 29[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s represent the sample standard deviation
[tex] ME= 2.1[/tex] represent the margin of error
n represent the sample size
Solution
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And this formula is equivalent to:
[tex] \bar X \pm ME[/te]x
The degrees of freedom are given by:
[tex]df=n-1=317-1=316[/tex]
And replaicing we got:
[tex]29-2.1=26.9[/tex]
[tex]29+2.1=31.1[/tex]
The 95% confidence interval would be between 26.9 and 31.1
3. Factor the expression.
d2 + 120 + 36
A (d + 6)2
B (d - 36)(0 - 1)
OC (d - 6)2
D (d + 6)(d - 6)
Answers
Answer:
The complete factored form of this equation is (d + 6)²
Step-by-step explanation:
The first step in factoring this equation is multiply the first term and the last term together. Out first term is d² and our last term is 36. Since d² does not have a coefficient, then we assume this number to be 1.
1 × 36 = 36
So, now we need to find two factors that multiply to 36 and add together to get 12. Two factors that best represents this is 6 and 6. So, we will plug these numbers into our equation. Replace 12d with 6d + 6d.
d² + 6d + 6d + 36
Group the first two terms together and the last two terms together.
(d² + 6d) + (6d + 36)
Now, find the greatest common factor of each parentheses and factor the terms.
d(d + 6) + 6(d + 6)
From looking at this, we can tell that this equation is a perfect squared equation. So, this means instead of writing both parentheses, we can just write one of the parentheses and square it.
So, the factored form of this equation is (d + 6)²
The equation of a circle is x2 + y2 = 56.25. Find the radius of the circle?
Answers
Answer:
r = 7.5
Step-by-step explanation:
Circle equation: [tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Since we are already give r², we simply just take the square root of 56.25, and we should get 7.5 as our final answer!
Find the Laplace transform F(s)=L{f(t)} of the function f(t)=sin2(wt), defined on the interval t≥0. F(s)=L{sin2(wt)}= help (formulas) Hint: Use a double-angle trigonometric identity. For what values of s does the Laplace transform exist? help (inequalities)
Answers
The Laplace transform of the function [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex] .
The Laplace transform exist when s > 0 .
Here, the given function is f(t) = sin²(wt) .
The Laplace transform of the the function f(t),
F(s) = f(t) = { [tex]{\frac{1}{2} \times 2sin^2(wt) }[/tex] }
F(s) = { [tex]\frac{1}{2} \times (1- cos2wt)[/tex] }
F(s) = { [tex]\frac{1}{2} - \frac{1}{2} \times cos(2wt)\\[/tex] }
F(s) = [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex]
Next,
The above Laplace transform exist if s > 0 .
Know more about Laplace transform,
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